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DeltaG is net energy available to do useful work and is thus a measure of "free energy". Show mathematically that DeltaG is a measure of free energy. Find the unit of DeltaG. If a reaction has positive enthalpy change and positive entropy change, under what condition will the reaction be spontaneous ? |
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Answer» Solution :Gibbs free energy is that thermodynamic quantity of a system, the decrease in whose value during a process is equal to the maximum POSSIBLE useful work that can be obtained from the system. Mathematically, this results may be derived as follows : The relationship between heat absorbed by a system Q, the change in its internal energy, `DeltaU` and the work done by the system is given by the equation of the first law of thermodynamics, therefore, `q= Delta U + W_("expansion") + W_("non-expansion") ...(i)` Under constant pressure condition, the expansion work is given by `pDeltaV`. `therefore Delta U + p Delta V = W_("non-expansion")` `= Delta H+ W_("non-expansion") ""...(ii)` For a reversible change taking place at constant temperature, `DeltaS= (q_("rev") )/( T) "or" q_("rev") = T Delta S""...(iii)` Substituting the value of q from Eq. (iii) in Eq. (ii), we get `T Delta S =Delta H + W_("non-expansion")` OR `Delta H - T Delta S =- W_("non-expansion") ""...(iv)` Substituting this value in equation (iv), we get `DeltaG= - W_("non-expansion") ""...(v)` THUS, free energy change can be taken as a measure of work other than the work of expansion. For most changes, the work of expansion can not be converted to other useful work, whereas the non-expansion work is convertible to useful work. Rearranging equation (v), it may be WRITTEN as `-Delta G= W_("non-expansion")= W_("useful")` As `- Delta G = W_("useful")` therefore, `Delta G` has the same units as those of work i.e., joule `Delta G = Delta H - T Delta S` If `Delta H = ` positive and `Delta S=` positive, then `DeltaG` will be negative i.e., process will be spontaneous only when `T DeltaS gt Delta H` in magnitude, which will be so when temperature is high. |
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